Q. The dimension of $k$ in the equation $W = \frac{1}{2}kx^{2}$ is
A) $\left\lbrack {ML}^{0}T^{- 2} \right\rbrack$
B) $\left\lbrack M^{0}{LT}^{- 1} \right\rbrack$
C) $\left\lbrack {MLT}^{- 2} \right\rbrack$
D) $\left\lbrack {ML}^{0}T^{- 1} \right\rbrack$
Explanation
Given, $W = \frac{1}{2}kx^{2}$ Writing the dimensions on both sides $\ \ \ \ \left\lbrack ML^{2}T^{- 2} \right\rbrack = \ k\left\lbrack M^{0}L^{2}T^{0} \right\rbrack$ $\therefore$ Dimensions of $k = \left\lbrack MT^{- 2} \right\rbrack = \left\lbrack {ML}^{0}T^{- 2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.